Heat a skillet over medium-high heat and brown the Italian sausage, breaking it up into smaller pieces. Once cooked, transfer the sausage to the slow cooker.
In the same skillet, sauté the onion, garlic, and carrots until they begin to soften, about 5 minutes. Transfer the mixture to the slow cooker.
Add the diced tomatoes, broth, white beans, dried thyme, dried oregano, red pepper flakes (if using), salt, and pepper to the slow cooker. Stir everything together to combine.
Cover the slow cooker and cook on low for 6 to 8 hours or on high for 3 to 4 hours. This will allow the flavors to meld together and the vegetables to become tender.
Just before serving, stir in the chopped spinach and allow it to wilt for a few minutes. Taste the soup and adjust the seasoning if needed.
Ladle the soup into bowls and garnish with grated Parmesan cheese and fresh parsley, if desired. Serve hot with crusty bread or a side salad.
